NCERT Solutions for Class 6 Maths Chapter 12: Ratio and Proportion - Exercise 12.2

Exercise 12.2

Refer to pages 3-6 for exercise 12.2 in the PDF

1. Determine if the following are in proportion.

(a) 15, 45, 40, 120

Ans: In order to check if the terms are in proportion, obtain the ratio of the first two terms as follows.

${\text{First term}}:{\text{Second term}} = 15:45$

$\dfrac{{{\text{First term}}}}{{{\text{Second term}}}} = \dfrac{{15}}{{45}}$

$\dfrac{{{\text{First term}}}}{{{\text{Second term}}}} = \dfrac{1}{3}$

${\text{First term}}:{\text{Second term}} = 1:3$

Therefore, 

$15:45 = 1:3$

Then obtain the ratio of last two terms as follows.

${\text{Third term}}:{\text{Fourth term}} = 40:120$

$\dfrac{{{\text{Third term}}}}{{{\text{Fourth term}}}} = \dfrac{{40}}{{120}}$

$\dfrac{{{\text{Third term}}}}{{{\text{Fourth term}}}} = \dfrac{1}{3}$

${\text{Third term}}:{\text{Fourth term}} = 1:3$

Therefore, 

$40:120 = 1:3$

Hence, 15, 45, 40, 120 are in proportion, since $15:45 = 1:3 = 40:120$.

(b) 33, 121, 9, 96

Ans: In order to check if the terms are in proportion, obtain the ratio of the first two terms as follows.

${\text{First term}}:{\text{Second term}} = 33:121$

$\dfrac{{{\text{First term}}}}{{{\text{Second term}}}} = \dfrac{{33}}{{121}}$

$\dfrac{{{\text{First term}}}}{{{\text{Second term}}}} = \dfrac{3}{{11}}$

${\text{First term}}:{\text{Second term}} = 3:11$

Therefore, 

$33:121 = 3:11$

Then obtain the ratio of last two terms as follows.

${\text{Third term}}:{\text{Fourth term}} = 9:96$

$\dfrac{{{\text{Third term}}}}{{{\text{Fourth term}}}} = \dfrac{9}{{96}}$

$\dfrac{{{\text{Third term}}}}{{{\text{Fourth term}}}} = \dfrac{3}{{32}}$

${\text{Third term}}:{\text{Fourth term}} = 3:32$

Therefore, 

$9:96 = 3:32$

Hence, 33, 121, 9, 96 are not in proportion, since $33:121 = 3:11 \ne 3:32 = 9:96$.

(c) 24, 28, 36, 48

Ans: In order to check if the terms are in proportion, obtain the ratio of the first two terms as follows.

${\text{First term}}:{\text{Second term}} = 24:28$

$\dfrac{{{\text{First term}}}}{{{\text{Second term}}}} = \dfrac{{24}}{{28}}$

$\dfrac{{{\text{First term}}}}{{{\text{Second term}}}} = \dfrac{6}{7}$

${\text{First term}}:{\text{Second term}} = 6:7$

Therefore, 

$24:28 = 6:7$

Then obtain the ratio of last two terms as follows.

${\text{Third term}}:{\text{Fourth term}} = 36:48$

$\dfrac{{{\text{Third term}}}}{{{\text{Fourth term}}}} = \dfrac{{36}}{{48}}$

$\dfrac{{{\text{Third term}}}}{{{\text{Fourth term}}}} = \dfrac{3}{4}$

${\text{Third term}}:{\text{Fourth term}} = 3:4$

Therefore, 

$36:48 = 3:4$

Hence, 24, 28, 36, 48 are not in proportion, since $24:28 = 6:7 \ne 3:4 = 36:48$.

(d) 32, 48, 70, 210

Ans: In order to check if the terms are in proportion, obtain the ratio of the first two terms as follows.

${\text{First term}}:{\text{Second term}} = 32:48$

$\dfrac{{{\text{First term}}}}{{{\text{Second term}}}} = \dfrac{{32}}{{48}}$

$\dfrac{{{\text{First term}}}}{{{\text{Second term}}}} = \dfrac{2}{3}$

${\text{First term}}:{\text{Second term}} = 2:3$

Therefore, 

$32:48 = 2:3$

Then obtain the ratio of last two terms as follows.

${\text{Third term}}:{\text{Fourth term}} = 70:210$

$\dfrac{{{\text{Third term}}}}{{{\text{Fourth term}}}} = \dfrac{{70}}{{210}}$

$\dfrac{{{\text{Third term}}}}{{{\text{Fourth term}}}} = \dfrac{1}{3}$

${\text{Third term}}:{\text{Fourth term}} = 1:3$

Therefore, 

$70:210 = 1:3$

Hence, 32, 48, 70, 210are not in proportion, since $32:48 = 2:3 \ne 1:3 = 70:210$.

(e) 4, 6, 8, 12

Ans: In order to check if the terms are in proportion, obtain the ratio of the first two terms as follows.

${\text{First term}}:{\text{Second term}} = 4:6$

$\dfrac{{{\text{First term}}}}{{{\text{Second term}}}} = \dfrac{4}{6}$

$\dfrac{{{\text{First term}}}}{{{\text{Second term}}}} = \dfrac{2}{3}$

${\text{First term}}:{\text{Second term}} = 2:3$

Therefore, 

$4:6 = 2:3$

Then obtain the ratio of last two terms as follows.

${\text{Third term}}:{\text{Fourth term}} = 8:12$

$\dfrac{{{\text{Third term}}}}{{{\text{Fourth term}}}} = \dfrac{8}{{12}}$

$\dfrac{{{\text{Third term}}}}{{{\text{Fourth term}}}} = \dfrac{2}{3}$

${\text{Third term}}:{\text{Fourth term}} = 2:3$

Therefore, 

$8:12 = 2:3$

Hence, 4, 6, 8, 12are in proportion, since $4:6 = 2:3 = 8:12$.

(f) 33, 44, 75, 100

Ans: In order to check if the terms are in proportion, obtain the ratio of the first two terms as follows.

${\text{First term}}:{\text{Second term}} = 33:44$

$\dfrac{{{\text{First term}}}}{{{\text{Second term}}}} = \dfrac{{33}}{{44}}$

$\dfrac{{{\text{First term}}}}{{{\text{Second term}}}} = \dfrac{3}{4}$

${\text{First term}}:{\text{Second term}} = 3:4$

Therefore, 

$33:44 = 3:4$

Then obtain the ratio of last two terms as follows.

${\text{Third term}}:{\text{Fourth term}} = 75:100$

$\dfrac{{{\text{Third term}}}}{{{\text{Fourth term}}}} = \dfrac{{75}}{{100}}$

$\dfrac{{{\text{Third term}}}}{{{\text{Fourth term}}}} = \dfrac{3}{4}$

${\text{Third term}}:{\text{Fourth term}} = 3:4$

Therefore, 

$75:100 = 3:4$

Hence, 33, 44, 75, 100are in proportion, since $33:44 = 3:4 = 75:100$.

2. Write True (T) or False ( F ) against each of the following statements :

(a) $16:24::20:30$

Ans: In order to check if the statement is true, obtain the ratio of the first two terms as follows.

${\text{First term}}:{\text{Second term}} = 16:24$

$\dfrac{{{\text{First term}}}}{{{\text{Second term}}}} = \dfrac{{16}}{{24}}$

$\dfrac{{{\text{First term}}}}{{{\text{Second term}}}} = \dfrac{2}{3}$

${\text{First term}}:{\text{Second term}} = 2:3$

Therefore, 

$16:24 = 2:3$

Then obtain the ratio of last two terms as follows.

${\text{Third term}}:{\text{Fourth term}} = 20:30$

$\dfrac{{{\text{Third term}}}}{{{\text{Fourth term}}}} = \dfrac{{20}}{{30}}$

$\dfrac{{{\text{Third term}}}}{{{\text{Fourth term}}}} = \dfrac{2}{3}$

${\text{Third term}}:{\text{Fourth term}} = 2:3$

Therefore, 

$20:30 = 2:3$

Since $16:24 = 2:3 = 20:30$, then $16:24$ and $20:30$ are in proportion. And consequently, the given statement $16:24::20:30$ is true.

(b) $21:6::35:10$

Ans: In order to check if the statement is true, obtain the ratio of the first two terms as follows.

${\text{First term}}:{\text{Second term}} = 21:6$

$\dfrac{{{\text{First term}}}}{{{\text{Second term}}}} = \dfrac{{21}}{6}$

$\dfrac{{{\text{First term}}}}{{{\text{Second term}}}} = \dfrac{7}{2}$

${\text{First term}}:{\text{Second term}} = 7:2$

Therefore, 

$21:6 = 7:2$

Then obtain the ratio of last two terms as follows.

${\text{Third term}}:{\text{Fourth term}} = 35:10$

$\dfrac{{{\text{Third term}}}}{{{\text{Fourth term}}}} = \dfrac{{35}}{{10}}$

$\dfrac{{{\text{Third term}}}}{{{\text{Fourth term}}}} = \dfrac{7}{2}$

${\text{Third term}}:{\text{Fourth term}} = 7:2$

Therefore, 

$35:10 = 7:2$

Since $21:6 = 7:2 = 35:10$, then $21:6$ and $35:10$ are in proportion. And consequently, the given statement $21:6::35:10$ is true.

(c) \[12:18::28:12\]

Ans: In order to check if the statement is true, obtain the ratio of the first two terms as follows.

${\text{First term}}:{\text{Second term}} = 12:18$

$\dfrac{{{\text{First term}}}}{{{\text{Second term}}}} = \dfrac{{12}}{{18}}$

$\dfrac{{{\text{First term}}}}{{{\text{Second term}}}} = \dfrac{2}{3}$

${\text{First term}}:{\text{Second term}} = 2:3$

Therefore, 

$12:18 = 2:3$

Then obtain the ratio of last two terms as follows.

${\text{Third term}}:{\text{Fourth term}} = 28:12$

$\dfrac{{{\text{Third term}}}}{{{\text{Fourth term}}}} = \dfrac{{28}}{{12}}$

$\dfrac{{{\text{Third term}}}}{{{\text{Fourth term}}}} = \dfrac{7}{3}$

${\text{Third term}}:{\text{Fourth term}} = 7:3$

Therefore, 

$28:12 = 7:3$

Since $12:18 = 2:3 \ne 7:3 = 28:12$, then $12:18$ and $28:12$ are not in proportion. And consequently, the given statement \[12:18::28:12\] is false.

(d) \[8:9::24:27\]

Ans: In order to check if the statement is true, obtain the ratio of the first two terms as follows.

${\text{First term}}:{\text{Second term}} = 8:9$

$\dfrac{{{\text{First term}}}}{{{\text{Second term}}}} = \dfrac{8}{9}$

${\text{First term}}:{\text{Second term}} = 8:9$

Therefore, 

$8:9 = 8:9$

Then obtain the ratio of last two terms as follows.

${\text{Third term}}:{\text{Fourth term}} = 24:27$

$\dfrac{{{\text{Third term}}}}{{{\text{Fourth term}}}} = \dfrac{{24}}{{27}}$

$\dfrac{{{\text{Third term}}}}{{{\text{Fourth term}}}} = \dfrac{8}{9}$

${\text{Third term}}:{\text{Fourth term}} = 8:9$

Therefore, 

$24:27 = 8:9$

Since $8:9 = 8:9 = 24:27$, then $8:9$ and $24:27$ are in proportion. And consequently, the given statement \[8:9::24:27\] is true.

(e) \[5.2:3.9::3:4\]

Ans: In order to check if the statement is true, obtain the ratio of the first two terms as follows.

${\text{First term}}:{\text{Second term}} = 5.2:3.9$

$\dfrac{{{\text{First term}}}}{{{\text{Second term}}}} = \dfrac{{5.2}}{{3.9}}$

$\dfrac{{{\text{First term}}}}{{{\text{Second term}}}} = \dfrac{{52}}{{39}}$

$\dfrac{{{\text{First term}}}}{{{\text{Second term}}}} = \dfrac{4}{3}$

${\text{First term}}:{\text{Second term}} = 4:3$

Therefore, 

$5.2:3.9 = 4:3$

Then obtain the ratio of last two terms as follows.

${\text{Third term}}:{\text{Fourth term}} = 3:4$

$\dfrac{{{\text{Third term}}}}{{{\text{Fourth term}}}} = \dfrac{3}{4}$

${\text{Third term}}:{\text{Fourth term}} = 3:4$

Therefore, 

\[3:4 = 3:4\]

Since $5.2:3.9 = 4:3 \ne 3:4 = 3:4$, then $5.2:3.9$ and $3:4$ are not in proportion. And consequently, the given statement \[5.2:3.9::3:4\] is false.

(f) \[0.9:0.36::10:4\]

Ans: In order to check if the statement is true, obtain the ratio of the first two terms as follows.

${\text{First term}}:{\text{Second term}} = 0.9:0.36$

$\dfrac{{{\text{First term}}}}{{{\text{Second term}}}} = \dfrac{{0.9}}{{0.36}}$

$\dfrac{{{\text{First term}}}}{{{\text{Second term}}}} = \dfrac{{90}}{{36}}$

$\dfrac{{{\text{First term}}}}{{{\text{Second term}}}} = \dfrac{5}{2}$

${\text{First term}}:{\text{Second term}} = 5:2$

Therefore, 

$0.9:0.36 = 5:2$

Then obtain the ratio of last two terms as follows.

${\text{Third term}}:{\text{Fourth term}} = 10:4$

$\dfrac{{{\text{Third term}}}}{{{\text{Fourth term}}}} = \dfrac{{10}}{4}$

$\dfrac{{{\text{Third term}}}}{{{\text{Fourth term}}}} = \dfrac{5}{2}$

${\text{Third term}}:{\text{Fourth term}} = 5:2$

Therefore, 

$10:4 = 5:2$

Since $0.9:0.36 = 5:2 = 10:4$, then $0.9:0.36$ and $10:4$ are in proportion. And consequently, the given statement \[0.9:0.36::10:4\] is true.

3. Are the following statements true?

(a) 40 persons : 200 persons = ₹ 15 : ₹ 75

Ans: In order to check if the statement is true, obtain the ratio of the first two terms as follows.

${\text{First term}}:{\text{Second term}} = 40:200$

$\dfrac{{{\text{First term}}}}{{{\text{Second term}}}} = \dfrac{{40}}{{200}}$

$\dfrac{{{\text{First term}}}}{{{\text{Second term}}}} = \dfrac{1}{5}$

${\text{First term}}:{\text{Second term}} = 1:5$

Therefore, 

$40:200 = 1:5$

Then obtain the ratio of last two terms as follows.

${\text{Third term}}:{\text{Fourth term}} = 15:75$

$\dfrac{{{\text{Third term}}}}{{{\text{Fourth term}}}} = \dfrac{{15}}{{75}}$

$\dfrac{{{\text{Third term}}}}{{{\text{Fourth term}}}} = \dfrac{1}{5}$

${\text{Third term}}:{\text{Fourth term}} = 1:5$

Therefore, 

$15:75 = 1:5$

Since $40:200 = 1:5 = 15:75$, then the given statement is true.

(b) $7.5$litres : 15 litres = 5 kg : 10 kg

Ans: In order to check if the statement is true, obtain the ratio of the first two terms as follows.

${\text{First term}}:{\text{Second term}} = 7.5:15$

$\dfrac{{{\text{First term}}}}{{{\text{Second term}}}} = \dfrac{{75}}{{150}}$

$\dfrac{{{\text{First term}}}}{{{\text{Second term}}}} = \dfrac{1}{2}$

${\text{First term}}:{\text{Second term}} = 1:2$

Therefore, 

$7.5:15 = 1:2$

Then obtain the ratio of last two terms as follows.

${\text{Third term}}:{\text{Fourth term}} = 5:10$

$\dfrac{{{\text{Third term}}}}{{{\text{Fourth term}}}} = \dfrac{5}{{10}}$

$\dfrac{{{\text{Third term}}}}{{{\text{Fourth term}}}} = \dfrac{1}{2}$

${\text{Third term}}:{\text{Fourth term}} = 1:2$

Therefore, 

$5:10 = 1:2$

Since $7.5:15 = 1:2 = 5:10$, then the given statement is true.

(c) 99 kg : 45 kg = ₹ 44 : ₹ 20

Ans: In order to check if the statement is true, obtain the ratio of the first two terms as follows.

${\text{First term}}:{\text{Second term}} = 99:45$

$\dfrac{{{\text{First term}}}}{{{\text{Second term}}}} = \dfrac{{99}}{{45}}$

$\dfrac{{{\text{First term}}}}{{{\text{Second term}}}} = \dfrac{{11}}{5}$

${\text{First term}}:{\text{Second term}} = 11:5$

Therefore, 

$99:45 = 11:5$

Then obtain the ratio of last two terms as follows.

${\text{Third term}}:{\text{Fourth term}} = 44:20$

$\dfrac{{{\text{Third term}}}}{{{\text{Fourth term}}}} = \dfrac{{44}}{{20}}$

$\dfrac{{{\text{Third term}}}}{{{\text{Fourth term}}}} = \dfrac{{11}}{5}$

${\text{Third term}}:{\text{Fourth term}} = 11:5$

Therefore, 

$44:20 = 11:5$

Since $99:45 = 11:5 = 44:20$, then the given statement is true.

(d) 32 m : 64 m = 6 sec : 12 sec

Ans:In order to check if the statement is true, obtain the ratio of the first two terms as follows.

${\text{First term}}:{\text{Second term}} = 32:64$

$\dfrac{{{\text{First term}}}}{{{\text{Second term}}}} = \dfrac{{32}}{{64}}$

$\dfrac{{{\text{First term}}}}{{{\text{Second term}}}} = \dfrac{1}{2}$

${\text{First term}}:{\text{Second term}} = 1:2$

Therefore,

$32:64 = 1:2$

Then obtain the ratio of last two terms as follows.

${\text{Third term}}:{\text{Fourth term}} = 6:12$

$\dfrac{{{\text{Third term}}}}{{{\text{Fourth term}}}} = \dfrac{6}{{12}}$

$\dfrac{{{\text{Third term}}}}{{{\text{Fourth term}}}} = \dfrac{1}{2}$

${\text{Third term}}:{\text{Fourth term}} = 1:2$

Therefore, 

$6:12 = 1:2$

Since $32:64 = 1:2 = 6:12$, then the given statement is true.

(e) 45 km : 60 km = 12 hours : 15 hours

Ans: In order to check if the statement is true, obtain the ratio of the first two terms as follows.

${\text{First term}}:{\text{Second term}} = 45:60$

$\dfrac{{{\text{First term}}}}{{{\text{Second term}}}} = \dfrac{{45}}{{60}}$

$\dfrac{{{\text{First term}}}}{{{\text{Second term}}}} = \dfrac{3}{4}$

${\text{First term}}:{\text{Second term}} = 3:4$

Therefore,

$45:60 = 3:4$

Then obtain the ratio of last two terms as follows.

${\text{Third term}}:{\text{Fourth term}} = 12:15$

$\dfrac{{{\text{Third term}}}}{{{\text{Fourth term}}}} = \dfrac{{12}}{{15}}$

$\dfrac{{{\text{Third term}}}}{{{\text{Fourth term}}}} = \dfrac{4}{5}$

${\text{Third term}}:{\text{Fourth term}} = 4:5$

Therefore, 

$12:15 = 4:5$

Since $45:60 = 3:4 \ne 4:5 = 12:15$, then the given statement is false.

4. Determine if the following ratios form a proportion. Also, write the middle terms and extreme terms where the ratios form a proportion.

(a) 25 cm : 1 m and ₹ 40 : ₹ 160

Ans: 1 m can be written as $1{\text{ m}} = 100{\text{ cm}}$.

Therefore the first ratio can be written as, $25{\text{ cm}}:1{\text{ m}} = 25{\text{ cm}}:100{\text{ cm}}$.

In order to check if the given ratios are in proportion, obtain the ratio of the first two terms as follows.

${\text{First term}}:{\text{Second term}} = 25:100$

$\dfrac{{{\text{First term}}}}{{{\text{Second term}}}} = \dfrac{{25}}{{100}}$

$\dfrac{{{\text{First term}}}}{{{\text{Second term}}}} = \dfrac{1}{4}$

${\text{First term}}:{\text{Second term}} = 1:4$

Therefore, 

$25:100 = 1:4$

Then obtain the ratio of last two terms as follows.

${\text{Third term}}:{\text{Fourth term}} = 40:160$

$\dfrac{{{\text{Third term}}}}{{{\text{Fourth term}}}} = \dfrac{{40}}{{160}}$

$\dfrac{{{\text{Third term}}}}{{{\text{Fourth term}}}} = \dfrac{1}{4}$

${\text{Third term}}:{\text{Fourth term}} = 1:4$

Therefore, 

$40:160 = 1:4$

Since $25:100 = 1:4 = 40:160$, the given ratios are in proportions.

If $a:b$ and $c:d$ are two ratios in proportions then $a,{\text{ }}d$ are the extreme terms and $b,{\text{ }}c$ are the middle terms.

Therefore, from the given ratios 1 m,₹ 40are the middle terms and 25 cm, ₹ 160 are the extreme terms.

(b) 39 litres : 65 litres and 6 bottles : 10 bottles

Ans: In order to check if the given ratios are in proportion, obtain the ratio of the first two terms as follows.

${\text{First term}}:{\text{Second term}} = 39:65$

$\dfrac{{{\text{First term}}}}{{{\text{Second term}}}} = \dfrac{{39}}{{65}}$

$\dfrac{{{\text{First term}}}}{{{\text{Second term}}}} = \dfrac{3}{5}$

${\text{First term}}:{\text{Second term}} = 3:5$

Therefore, 

$39:65 = 3:5$

Then obtain the ratio of last two terms as follows.

${\text{Third term}}:{\text{Fourth term}} = 6:10$

$\dfrac{{{\text{Third term}}}}{{{\text{Fourth term}}}} = \dfrac{6}{{10}}$

$\dfrac{{{\text{Third term}}}}{{{\text{Fourth term}}}} = \dfrac{3}{5}$

${\text{Third term}}:{\text{Fourth term}} = 3:5$

Therefore, 

$6:10 = 3:5$

Since $39:65 = 3:5 = 6:10$, the given ratios are in proportions.

If $a:b$ and $c:d$ are two ratios in proportions then $a,{\text{ }}d$ are the extreme terms and $b,{\text{ }}c$ are the middle terms.

Therefore, from the given ratios 65 litres, 6 bottles are the middle terms and 39 litres, 10 bottles  are the extreme terms.

(c) 2 kg : 80 kg and 25 g : 625 g

Ans: In order to check if the given ratios are in proportion, obtain the ratio of the first two terms as follows.

${\text{First term}}:{\text{Second term}} = 2:80$

$\dfrac{{{\text{First term}}}}{{{\text{Second term}}}} = \dfrac{2}{{80}}$

$\dfrac{{{\text{First term}}}}{{{\text{Second term}}}} = \dfrac{1}{{40}}$

${\text{First term}}:{\text{Second term}} = 1:40$

Therefore, 

$2:80 = 1:40$

Then obtain the ratio of last two terms as follows.

${\text{Third term}}:{\text{Fourth term}} = 25:625$

$\dfrac{{{\text{Third term}}}}{{{\text{Fourth term}}}} = \dfrac{{25}}{{625}}$

$\dfrac{{{\text{Third term}}}}{{{\text{Fourth term}}}} = \dfrac{1}{{25}}$

${\text{Third term}}:{\text{Fourth term}} = 1:25$

Therefore, 

$25:125 = 1:25$

Since $2:80 = 1:40 \ne 1:25 = 25:625$, the given ratios are not in proportions.

(d) 200 ml :$2.5$ litre and ₹ 4 : ₹ 50

Ans: 1 litre can be written as $1{\text{ litre}} = 1000{\text{ mL}}$.

Therefore, 

$2.5{\text{ litre}} = 2.5 \times 1000{\text{ ml}}$

$2.5{\text{ litre}} = 2500{\text{ ml}}$

Therefore the first ratio can be written as, \[200{\text{ ml}}:2.5{\text{ litre}} = 200{\text{ ml}}:2500{\text{ ml}}\].

In order to check if the given ratios are in proportion, obtain the ratio of the first two terms as follows.

${\text{First term}}:{\text{Second term}} = 200:2500$

$\dfrac{{{\text{First term}}}}{{{\text{Second term}}}} = \dfrac{{200}}{{2500}}$

$\dfrac{{{\text{First term}}}}{{{\text{Second term}}}} = \dfrac{2}{{25}}$

${\text{First term}}:{\text{Second term}} = 2:25$

Therefore, 

$200:2500 = 2:25$

Then obtain the ratio of last two terms as follows.

${\text{Third term}}:{\text{Fourth term}} = 4:50$

$\dfrac{{{\text{Third term}}}}{{{\text{Fourth term}}}} = \dfrac{4}{{50}}$

$\dfrac{{{\text{Third term}}}}{{{\text{Fourth term}}}} = \dfrac{2}{{25}}$

${\text{Third term}}:{\text{Fourth term}} = 2:25$

Therefore, 

$4:50 = 2:25$

Since $200:2500 = 2:25 = 4:50$, the given ratios are in proportions.

If $a:b$ and $c:d$ are two ratios in proportions then $a,{\text{ }}d$ are the extreme terms and $b,{\text{ }}c$ are the middle terms.

Therefore, from the given ratios $2.5$ litres, ₹ 4are the middle terms and 200 ml, ₹ 50 are the extreme terms.

NCERT Solutions for Class 6 Maths Chapter 12 Ratio and Proportion Exercise 12.2

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